The growth rates of Si(001) and Ge(001) by gas-source molecular-beam epitaxy (GS-MBE) from $\rm Si\sb2H\sb6$ and $\rm Ge\sb2H\sb6$ as a function of T$\sb{\rm s}$ are well described by a model based upon dissociative $\rm Si\sb2H\sb6$ and $\rm Ge\sb2H\sb6$ chemisorption followed by a series of surface decomposition reactions with the rate-limiting step being first-order hydrogen desorption from Si and Ge monohydride for which the activation energy is 2.04 and 1.56 eV, respectively. The zero-coverage reactive sticking probability of $\rm Si\sb2H\sb6$ on Si(001)2 x 1 ($\rm Ge\sb2H\sb6$ on Ge(001)2 x 1) in the impingement-flux-limited growth regime was found to be $\rm S\sbsp{Si\sb2H\sb6}{Si} = 0.036\ (S\sbsp{Ge\sb2H\sb6}{Ge} = 0.052).$ The growth rate of $\rm Si\sb{1-x}Ge\sb{x}$ alloys R$\sb{\rm SiGe}$ decreases somewhat with increasing $\rm G\sb2H\sb6$ in the flux-limited growth mode while dramatically increasing $\rm R\sb{SiGe}$ in the surface-reaction-limited regime.B-doped Si(001), Ge(001), and $\rm Si\sb{1-x}Ge\sb{x}(001)2 x 1$ films were grown on Si(001) and Ge(001) substrates by GS-MBE using $\rm Si\sb2H\sb6,\ Ge\sb2H\sb6$, and $\rm B\sb2H\sb6.$ For constant $\rm Si\sb2H\sb6$ and/or $\rm Ge\sb2H\sb6$ fluxes, B concentrations $\rm C\sb{B}\ (5\times 10\sp{16}-5\times 10\sp{19}\ cm\sp{-3})$ were found to increase linearly with increasing flux $\rm B\sb2H\sb6$ at constant film growth temperatures T$\rm\sb{s}$ and to decrease exponentially with 1/T$\sb{\rm s}$ at constant $\rm B\sb2H\sb6$ fluxes. $\rm B\sb2H\sb6$ reactive sticking probabilities ranged from $\simeq 6.4\times 10\sp{-4}$ at T$\rm\sb{s} = 600\sp\circ C$ to $1.4\times 10\sp{-3}$ at 950$\sp\circ$C for B doped Si(001) and from $8\times10\sp{-4}$ at 300$\sp\circ$C to $2\times10\sp{-5}$ at 400$\sp\circ$ for B doped Ge(001).Structural analysis by in-situ reflection high energy electron diffraction combined with post-deposition high-resolution plan-view and cross-sectional transmission electron microscopy, high-resolution X-ray diffraction, and reciprocal lattice mapping showed that all films were high-quality single crystals.A comparison of quantitative secondary-ion mass spectrometry (SIMS) and temperature-dependent Hall-effect measurements showed that B was incorporated into substitutional electrically-active sites under all growth conditions investigated. SIMS B depth-profiles from modulation-doped samples were abrupt with no indication of surface segregation and $\delta$-doped layers were grown. The hole drift mobility in fully-strained alloys was found to increase while the Hall mobility decreased with increasing Ge fraction yielding a Hall scattering factor $\gamma$ which ranged from 0.77 for Si to 0.26 for alloys with x = 0.28. Room-temperature hole mobilities were equal to the best reported bulk $\rm Si\sb{1-x}Ge\sb{x}{:}B$ values and ranged, with p = $2\rm\times 10\sp{18}\ cm\sp{-3}$ for example, from 160 cm$\rm\sp2V\sp{-1} s\sp{-1}$ for x = 0.28 to 110 $\rm cm\sp2V\sp{-1}s\sp{-1}$ for x = 0.05 to 86 for pure Si.